Current range characteristics of Swiss stone pine (Pinus cembra L.) along the Carpathians revealed by chloroplast SSR markers.

We investigated the diversity pattern of nine Swiss stone pine (Pinus cembra L.) populations along the Carpathian range including the High Tatras, by using six chloroplast DNA microsatellites (cpSSR). Our aim was to detect genetically distinct regions by clustering of populations, and to tackle possible historical colonization routes. Our analysis referred to an investigated geographical range with the two most distant populations situated at about 500 air km. We found that the most diverse populations are situated at the two edges of the investigated part, in the Retezat Mts. (South Carpathians) and the High Tatras, and diversity decreases towards the populations of the Eastern Carpathians. Hierarchical clustering and NMDS revealed that the populations of the South Carpathians with the Tatras form a distinct cluster, significantly separated from those of the Eastern Carpathians. Moreover, based on the most variable chloroplast microsatellites, the four populations of the two range edges are not significantly different. Our results, supported also by palynological and late glacial macrofossil evidences, indicate refugial territories within the Retezat Mts. that conserved rich haplotype composition. From this refugial territory Pinus cembra might have colonized the Eastern Carpathians, and this was accompanied by a gradual decrease in population diversity. Populations of the High Tatras might have had the same role in the colonizing events of the Carpathians, as positive correlation was detected among populations lying from each other at a distance of 280 km, the maximum distance between neighbouring populations

On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.Comment: 37 page

Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform

We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR_IHN, peak-to-average power ratio with respect to the {I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figure

Hidden magnetic order in CuNCN

We report a comprehensive experimental and theoretical study of the quasi-one-dimensional quantum magnet CuNCN. Based on magnetization measurements above room temperature as well as muon spin rotation and electron spin resonance measurements, we unequivocally establish the localized Cu+2-based magnetism and the magnetic transition around 70 K, both controversially discussed in the previous literature. Thermodynamic data conform to the uniform-spin-chain model with a nearest-neighbor intrachain coupling of about 2300 K, in remarkable agreement with the microscopic magnetic model based on density functional theory band-structure calculations. Using exact diagonalization and the coupled-cluster method, we derive a collinear antiferromagnetic order with a strongly reduced ordered moment of about 0.4 mu_B, indicating strong quantum fluctuations inherent to this quasi-one-dimensional spin system. We re-analyze the available neutron-scattering data, and conclude that they are not sufficient to resolve or disprove the magnetic order in CuNCN. By contrast, spectroscopic techniques indeed show signatures of long-range magnetic order below 70 K, yet with a rather broad distribution of internal field probed by implanted muons. We contemplate the possible structural origin of this effect and emphasize peculiar features of the microstructure studied with synchrotron powder x-ray diffraction.Comment: 17 pages, 17 figures, 1 tabl

Mid-Pleistocene and Holocene demographic fluctuation of Scots pine (Pinus sylvestris L.) in the Carpathian Mountains and the Pannonian Basin: Signs of historical expansions and contractions

Climate fluctuations of the Quaternary caused radical changes in distribution of tree species and resulted in large-scale range shifts, population contractions and expansions. Scots pine (Pinus sylvestris L.) a widely distributed conifer of the boreal regions underwent spatio-temporal changes, which shaped the modern-day genetic structure and phylogeographic pattern of the species. By applying independent approaches, including molecular genetic data and historical climate models we aimed to describe demography and past distribution patterns of Scots pine populations from the highly fragmented southern periphery, the Carpathians and the Pannonian Basin. We used Approximate Bayesian Computation (ABC) approach based on nuclear microsatellite markers (nSSRs) and Maximum Entropy distribution modelling (MaxEnt) with temperature- and precipitation-related bioclimatic data. ABC results indicated that from an ancestral Scots pine population two genetic lineages have diverged that in the Mid-Pleistocene due to the favourable climatic conditions underwent population expansion leading to an admixture event. The outcome of the hindcasting confirmed the expansion that leaded to the admixture event revealed by the ABC analysis. This can be dated to the Late Glacial period (14,160–11,800 yrs BP), in which widespread distribution of Scots pine in accordance with palynological proxies was detected. Predictions for the Mid-Holocene period have shown large-scale reduction in distribution of Scots pine and low probability of its occurrence, leading to disjunction and population fragmentation

On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12

We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these codes can be represented as graphs, and that two codes are equivalent if and only if the corresponding graphs are equivalent with respect to local complementation and graph isomorphism. We use these facts to classify all codes of length up to 12, where previously only all codes of length up to 9 were known. We also classify all extremal Type II codes of length 14. Finally, we find that the smallest Type I and Type II codes with trivial automorphism group have length 9 and 12, respectively.Comment: 18 pages, 4 figure

Three-dimensional AdS gravity and extremal CFTs at c=8m

We note that Witten's proposed duality between extremal c=24k CFTs and three-dimensional anti-de Sitter gravity may possibly be extended to central charges that are multiples of 8, for which extremal self-dual CFTs are known to exist up to c=40. All CFTs of this type with central charge 24 or higher, provided that they exist, have the required mass gap and may serve as candidate duals to three-dimensional gravity at the corresponding values of the cosmological constant. Here, we compute the genus one partition function of these theories up to c=88, we give exact and approximate formulas for the degeneracies of states, and we determine the genus two partition functions of the theories up to c=40.Comment: 17 pages, harvmac; v2: references added, version accepted in JHE